Testprep数学精解
THE CONCLUSION, "THE STRIKERS SHOULD ACCEPT THE MANAGEMENT’S OFFER," IS STAT
ED IN THE FIRST SENTENCE. THEN "ADMITTEDLY" INTRODUCES A CONCESSION; NAMELY,
THAT THE OFFER WAS LESS THAN WHAT WAS DEMANDED. THIS WEAKENS THE SPEAKER’S
CASE, BUT IT ADDRESSES A POTENTIAL CRITICISM OF HIS POSITION BEFORE IT CAN B
E MADE. THE LAST TWO SENTENCES OF THE ARGUMENT PRESENT MORE COMPELLING REASO
NS TO ACCEPT THE OFFER AND FORM THE GIST OF THE ARGUMENT.
FOLLOWING ARE SOME OF THE MOST COMMON COUNTER-PREMISE INDICATORS:
COUNTER-PREMISE INDICATORS
BUT DESPITE
ADMITTEDLY EXCEPT
EVEN THOUGH NONETHELESS
NEVERTHELESS ALTHOUGH
HOWEVER IN SPITE OF THE FACT
AS YOU MAY HAVE ANTICIPATED, THE GMAT WRITERS SOMETIMES USE COUNTER-PREMISES
TO BAIT WRONG ANSWER-CHOICES. ANSWER-CHOICES THAT REFER TO COUNTER-PREMISES
ARE VERY TEMPTING BECAUSE THEY REFER DIRECTLY TO THE PASSAGE AND THEY ARE I
N PART TRUE. BUT YOU MUST ASK YOURSELF "IS THIS THE MAIN POINT THAT THE AUTH
OR IS TRYING TO MAKE?" IT MAY MERELY BE A MINOR CONCESSION.
LOGIC II (DIAGRAMMING)
MOST ARGUMENTS ARE BASED ON SOME VARIATION OF AN IF-THEN STATEMENT. HOWEVER,
THE IF-THEN STATEMENT IS OFTEN EMBEDDED IN OTHER EQUIVALENT STRUCTURES. DIA
GRAMMING BRINGS OUT THE SUPERSTRUCTURE AND THE UNDERLYING SIMPLICITY OF ARGU
MENTS.
IF-THEN
A-->B
BY NOW YOU SHOULD BE WELL AWARE THAT IF THE PREMISE OF AN IF-THEN STATEMENT
IS TRUE THEN THE CONCLUSION MUST BE TRUE AS WELL. THIS IS THE DEFINING CHARA
CTERISTIC OF A CONDITIONAL STATEMENT; IT CAN BE ILLUSTRATED AS FOLLOWS:
A-->B
A
THEREFORE, B
THIS DIAGRAM DISPLAYS THE IF-THEN STATEMENT "A-->B," THE AFFIRMED PREMISE "A
," AND THE NECESSARY CONCLUSION "B." SUCH A DIAGRAM CAN BE VERY HELPFUL IN S
HOWING THE LOGICAL STRUCTURE OF AN ARGUMENT.
EXAMPLE: (IF-THEN)
IF JANE DOES NOT STUDY FOR THE GMAT, THEN SHE WILL NOT SCORE WELL. JANE, IN
FACT, DID NOT STUDY FOR THE GMAT; THEREFORE SHE SCORED POORLY ON THE TEST.
WHEN SYMBOLIZING GAMES, WE LET A LETTER STAND FOR AN ELEMENT. WHEN SYMBOLIZI
NG ARGUMENTS, HOWEVER, WE MAY LET A LETTER STAND FOR AN ELEMENT, A PHRASE, A
CLAUSE, OR EVEN AN ENTIRE SENTENCE. THE CLAUSE "JANE DOES NOT STUDY FOR THE
GMAT" CAN BE SYMBOLIZED AS ~S, AND THE CLAUSE "SHE WILL NOT SCORE WELL" CAN
BE SYMBOLIZED AS ~W. SUBSTITUTING THESE SYMBOLSSINTOSTHE ARGUMENT YIELDS TH
E FOLLOWING DIAGRAM:
~S-->~W
~S
THEREFORE, ~W
THIS DIAGRAM SHOWS THAT THE ARGUMENT HAS A VALID IF-THEN STRUCTURE. A CONDIT
IONAL STATEMENT IS PRESENTED, ~S-->~W; ITS PREMISE AFFIRMED, ~S; AND THEN TH
E CONCLUSION THAT NECESSARILY FOLLOWS, ~W, IS STATED.
EMBEDDED IF-THEN STATEMENTS
USUALLY, ARGUMENTS INVOLVE AN IF-THEN STATEMENT. UNFORTUNATELY, THE IF-THEN
THOUGHT IS OFTEN EMBEDDED IN OTHER EQUIVALENT STRUCTURES. IN THIS SECTION, W
E STUDY HOW TO SPOT THESE STRUCTURES.
EXAMPLE: (EMBEDDED IF-THEN)
JOHN AND KEN CANNOT BOTH GO TO THE PARTY.
AT FIRST GLANCE, THIS SENTENCE DOES NOT APPEAR TO CONTAIN AN IF-THEN STATEME
NT. BUT IT ESSENTIALLY SAYS: "IF JOHN GOES TO THE PARTY, THEN KEN DOES NOT."
EXAMPLE: (EMBEDDED IF-THEN)
DANIELLE WILL BE ACCEPTED TO GRADUATE SCHOOL ONLY IF SHE DOES WELL ON THE GR
E.
GIVEN THIS STATEMENT, WE KNOW THAT IF DANIELLE IS ACCEPTED TO GRADUATE SCHOO
L, THEN SHE MUST HAVE DONE WELL ON THE GRE. NOTE: STUDENTS OFTEN WRONGLY INT
ERPRET THIS STATEMENT TO MEAN:
"IF DANIELLE DOES WELL ON THE GRE, THEN SHE WILL BE ACCEPTED TO GRADUATE SCH
OOL."
THERE IS NO SUCH GUARANTEE. THE ONLY GUARANTEE IS THAT IF SHE DOES NOT DO WE
LL ON THE GRE, THEN SHE WILL NOT BE ACCEPTED TO GRADUATE SCHOOL.
"A ONLY IF B" IS LOGICALLY EQUIVALENT TO "IF A, THEN B."
AFFIRMING THE CONCLUSION FALLACY
A-->B
B
THEREFORE, A
REMEMBER THAT AN IF-THEN STATEMENT, A-->B, TELLS US ONLY TWO THINGS: (1) IF
A IS TRUE, THEN B IS TRUE AS WELL. (2) IF B IS FALSE, THEN A IS FALSE AS WEL
L (CONTRAPOSITIVE). IF, HOWEVER, WE KNOW THE CONCLUSION IS TRUE, THE IF-THEN
STATEMENT TELLS US NOTHING ABOUT THE PREMISE. AND IF WE KNOW THAT THE PREMI
SE IS FALSE (WE WILL CONSIDER THIS NEXT), THEN THE IF-THEN STATEMENT TELLS U
S NOTHING ABOUT THE CONCLUSION.
EXAMPLE: (AFFIRMING THE CONCLUSION FALLACY)
IF HE IS INNOCENT, THEN WHEN WE HOLD HIM UNDER WATER FOR SIXTY SECONDS HE WI
LL NOT DROWN. SINCE HE DID NOT DIE WHEN WE DUNKED HIM IN THE WATER, HE MUST
BE INNOCENT.